#include "math.h"

#include "float.h"
#include "stdio.h"

/* Get two 32 bit ints from a double */
#define EXTRACT_WORDS(hi, lo, d) \
  do {                           \
    union {                      \
      double f;                  \
      uint64_t i;                \
    } __u;                       \
    __u.f = (d);                 \
    (hi) = __u.i >> 32;          \
    (lo) = (uint32_t)__u.i;      \
  } while (0)

/* Get the more significant 32 bit int from a double */
#define GET_HIGH_WORD(hi, d) \
  do {                       \
    union {                  \
      double f;              \
      uint64_t i;            \
    } __u;                   \
    __u.f = (d);             \
    (hi) = __u.i >> 32;      \
  } while (0)

/* Get the less significant 32 bit int from a double */
#define GET_LOW_WORD(lo, d) \
  do {                      \
    union {                 \
      double f;             \
      uint64_t i;           \
    } __u;                  \
    __u.f = (d);            \
    (lo) = (uint32_t)__u.i; \
  } while (0)

/* Set a double from two 32 bit ints */
#define INSERT_WORDS(d, hi, lo)                      \
  do {                                               \
    union {                                          \
      double f;                                      \
      uint64_t i;                                    \
    } __u;                                           \
    __u.i = ((uint64_t)(hi) << 32) | (uint32_t)(lo); \
    (d) = __u.f;                                     \
  } while (0)

/* Set the more significant 32 bits of a double from an int */
#define SET_HIGH_WORD(d, hi)       \
  do {                             \
    union {                        \
      double f;                    \
      uint64_t i;                  \
    } __u;                         \
    __u.f = (d);                   \
    __u.i &= 0xffffffff;           \
    __u.i |= (uint64_t)(hi) << 32; \
    (d) = __u.f;                   \
  } while (0)

/* Set the less significant 32 bits of a double from an int */
#define SET_LOW_WORD(d, lo)         \
  do {                              \
    union {                         \
      double f;                     \
      uint64_t i;                   \
    } __u;                          \
    __u.f = (d);                    \
    __u.i &= 0xffffffff00000000ull; \
    __u.i |= (uint32_t)(lo);        \
    (d) = __u.f;                    \
  } while (0)

/* Get a 32 bit int from a float */
#define GET_FLOAT_WORD(w, d) \
  do {                       \
    union {                  \
      float f;               \
      uint32_t i;            \
    } __u;                   \
    __u.f = (d);             \
    (w) = __u.i;             \
  } while (0)

/* Set a float from a 32 bit int */
#define SET_FLOAT_WORD(d, w) \
  do {                       \
    union {                  \
      float f;               \
      uint32_t i;            \
    } __u;                   \
    __u.i = (w);             \
    (d) = __u.f;             \
  } while (0)

#define EPS DBL_EPSILON
#define FORCE_EVAL(x)                                   \
  do {                                                  \
    if (sizeof(x) == sizeof(float)) {                   \
      volatile float __x __attribute__((unused));       \
      __x = (x);                                        \
    } else if (sizeof(x) == sizeof(double)) {           \
      volatile double __x __attribute__((unused));      \
      __x = (x);                                        \
    } else {                                            \
      volatile long double __x __attribute__((unused)); \
      __x = (x);                                        \
    }                                                   \
  } while (0)

static const double_t toint = 1 / EPS;

double floor(double x) {
  union {
    double f;
    uint64_t i;
  } u = {x};
  int e = u.i >> 52 & 0x7ff;
  double_t y;

  if (e >= 0x3ff + 52 || x == 0) return x;
  /* y = int(x) - x, where int(x) is an integer neighbor of x */
  if (u.i >> 63)
    y = x - toint + toint - x;
  else
    y = x + toint - toint - x;
  /* special case because of non-nearest rounding modes */
  if (e <= 0x3ff - 1) {
    FORCE_EVAL(y);
    return u.i >> 63 ? -1 : 0;
  }
  if (y > 0) return x + y - 1;
  return x + y;
}

double frexp(double x, int *e) {
  union {
    double d;
    uint64_t i;
  } y = {x};
  int ee = y.i >> 52 & 0x7ff;

  if (!ee) {
    if (x) {
      x = frexp(x * 0x1p64, e);
      *e -= 64;
    } else
      *e = 0;
    return x;
  } else if (ee == 0x7ff) {
    return x;
  }

  *e = ee - 0x3fe;
  y.i &= 0x800fffffffffffffull;
  y.i |= 0x3fe0000000000000ull;
  return y.d;
}

double modf(double x, double *iptr) {
  union {
    double f;
    uint64_t i;
  } u = {x};
  uint64_t mask;
  int e = (int)(u.i >> 52 & 0x7ff) - 0x3ff;

  /* no fractional part */
  if (e >= 52) {
    *iptr = x;
    if (e == 0x400 && u.i << 12 != 0) /* nan */
      return x;
    u.i &= 1ULL << 63;
    return u.f;
  }

  /* no integral part*/
  if (e < 0) {
    u.i &= 1ULL << 63;
    *iptr = u.f;
    return x;
  }

  mask = -1ULL >> 12 >> e;
  if ((u.i & mask) == 0) {
    *iptr = x;
    u.i &= 1ULL << 63;
    return u.f;
  }
  u.i &= ~mask;
  *iptr = u.f;
  return x - u.f;
}

static const double bp[] =
    {
        1.0,
        1.5,
},
                    dp_h[] =
                        {
                            0.0,
                            5.84962487220764160156e-01,
}, /* 0x3FE2B803, 0x40000000 */
    dp_l[] =
        {
            0.0,
            1.35003920212974897128e-08,
},                              /* 0x3E4CFDEB, 0x43CFD006 */
    two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
    huge = 1.0e300, tiny = 1.0e-300,
                    /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
    L1 = 5.99999999999994648725e-01,     /* 0x3FE33333, 0x33333303 */
    L2 = 4.28571428578550184252e-01,     /* 0x3FDB6DB6, 0xDB6FABFF */
    L3 = 3.33333329818377432918e-01,     /* 0x3FD55555, 0x518F264D */
    L4 = 2.72728123808534006489e-01,     /* 0x3FD17460, 0xA91D4101 */
    L5 = 2.30660745775561754067e-01,     /* 0x3FCD864A, 0x93C9DB65 */
    L6 = 2.06975017800338417784e-01,     /* 0x3FCA7E28, 0x4A454EEF */
    P1 = 1.66666666666666019037e-01,     /* 0x3FC55555, 0x5555553E */
    P2 = -2.77777777770155933842e-03,    /* 0xBF66C16C, 0x16BEBD93 */
    P3 = 6.61375632143793436117e-05,     /* 0x3F11566A, 0xAF25DE2C */
    P4 = -1.65339022054652515390e-06,    /* 0xBEBBBD41, 0xC5D26BF1 */
    P5 = 4.13813679705723846039e-08,     /* 0x3E663769, 0x72BEA4D0 */
    lg2 = 6.93147180559945286227e-01,    /* 0x3FE62E42, 0xFEFA39EF */
    lg2_h = 6.93147182464599609375e-01,  /* 0x3FE62E43, 0x00000000 */
    lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
    ovt = 8.0085662595372944372e-017,    /* -(1024-log2(ovfl+.5ulp)) */
    cp = 9.61796693925975554329e-01,     /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
    cp_h = 9.61796700954437255859e-01,   /* 0x3FEEC709, 0xE0000000 =(float)cp */
    cp_l =
        -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
    ivln2 = 1.44269504088896338700e+00,   /* 0x3FF71547, 0x652B82FE =1/ln2 */
    ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
    ivln2_l =
        1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

double pow(double x, double y) {
  double z, ax, z_h, z_l, p_h, p_l;
  double y1, t1, t2, r, s, t, u, v, w;
  int32_t i, j, k, yisint, n;
  int32_t hx, hy, ix, iy;
  uint32_t lx, ly;

  EXTRACT_WORDS(hx, lx, x);
  EXTRACT_WORDS(hy, ly, y);
  ix = hx & 0x7fffffff;
  iy = hy & 0x7fffffff;

  /* x**0 = 1, even if x is NaN */
  if ((iy | ly) == 0) return 1.0;
  /* 1**y = 1, even if y is NaN */
  if (hx == 0x3ff00000 && lx == 0) return 1.0;
  /* NaN if either arg is NaN */
  if (ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) || iy > 0x7ff00000 ||
      (iy == 0x7ff00000 && ly != 0))
    return x + y;

  /* determine if y is an odd int when x < 0
   * yisint = 0       ... y is not an integer
   * yisint = 1       ... y is an odd int
   * yisint = 2       ... y is an even int
   */
  yisint = 0;
  if (hx < 0) {
    if (iy >= 0x43400000)
      yisint = 2; /* even integer y */
    else if (iy >= 0x3ff00000) {
      k = (iy >> 20) - 0x3ff; /* exponent */
      if (k > 20) {
        uint32_t j = ly >> (52 - k);
        if ((j << (52 - k)) == ly) yisint = 2 - (j & 1);
      } else if (ly == 0) {
        uint32_t j = iy >> (20 - k);
        if ((j << (20 - k)) == iy) yisint = 2 - (j & 1);
      }
    }
  }

  /* special value of y */
  if (ly == 0) {
    if (iy == 0x7ff00000) {              /* y is +-inf */
      if (((ix - 0x3ff00000) | lx) == 0) /* (-1)**+-inf is 1 */
        return 1.0;
      else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
        return hy >= 0 ? y : 0.0;
      else /* (|x|<1)**+-inf = 0,inf */
        return hy >= 0 ? 0.0 : -y;
    }
    if (iy == 0x3ff00000) { /* y is +-1 */
      if (hy >= 0) return x;
      y = 1 / x;
#if FLT_EVAL_METHOD != 0
      {
        union {
          double f;
          uint64_t i;
        } u = {y};
        uint64_t i = u.i & -1ULL / 2;
        if (i >> 52 == 0 && (i & (i - 1))) FORCE_EVAL((float)y);
      }
#endif
      return y;
    }
    if (hy == 0x40000000) /* y is 2 */
      return x * x;
    if (hy == 0x3fe00000) { /* y is 0.5 */
      if (hx >= 0)          /* x >= +0 */
        return sqrt(x);
    }
  }

  ax = fabs(x);
  /* special value of x */
  if (lx == 0) {
    if (ix == 0x7ff00000 || ix == 0 ||
        ix == 0x3ff00000) { /* x is +-0,+-inf,+-1 */
      z = ax;
      if (hy < 0) /* z = (1/|x|) */
        z = 1.0 / z;
      if (hx < 0) {
        if (((ix - 0x3ff00000) | yisint) == 0) {
          z = (z - z) / (z - z); /* (-1)**non-int is NaN */
        } else if (yisint == 1)
          z = -z; /* (x<0)**odd = -(|x|**odd) */
      }
      return z;
    }
  }

  s = 1.0; /* sign of result */
  if (hx < 0) {
    if (yisint == 0) /* (x<0)**(non-int) is NaN */
      return (x - x) / (x - x);
    if (yisint == 1) /* (x<0)**(odd int) */
      s = -1.0;
  }

  /* |y| is huge */
  if (iy > 0x41e00000) {   /* if |y| > 2**31 */
    if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
      if (ix <= 0x3fefffff) return hy < 0 ? huge * huge : tiny * tiny;
      if (ix >= 0x3ff00000) return hy > 0 ? huge * huge : tiny * tiny;
    }
    /* over/underflow if x is not close to one */
    if (ix < 0x3fefffff) return hy < 0 ? s * huge * huge : s * tiny * tiny;
    if (ix > 0x3ff00000) return hy > 0 ? s * huge * huge : s * tiny * tiny;
    /* now |1-x| is tiny <= 2**-20, suffice to compute
       log(x) by x-x^2/2+x^3/3-x^4/4 */
    t = ax - 1.0; /* t has 20 trailing zeros */
    w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
    u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
    v = t * ivln2_l - w * ivln2;
    t1 = u + v;
    SET_LOW_WORD(t1, 0);
    t2 = v - (t1 - u);
  } else {
    double ss, s2, s_h, s_l, t_h, t_l;
    n = 0;
    /* take care subnormal number */
    if (ix < 0x00100000) {
      ax *= two53;
      n -= 53;
      GET_HIGH_WORD(ix, ax);
    }
    n += ((ix) >> 20) - 0x3ff;
    j = ix & 0x000fffff;
    /* determine interval */
    ix = j | 0x3ff00000; /* normalize ix */
    if (j <= 0x3988E)    /* |x|<sqrt(3/2) */
      k = 0;
    else if (j < 0xBB67A) /* |x|<sqrt(3)   */
      k = 1;
    else {
      k = 0;
      n += 1;
      ix -= 0x00100000;
    }
    SET_HIGH_WORD(ax, ix);

    /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
    u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
    v = 1.0 / (ax + bp[k]);
    ss = u * v;
    s_h = ss;
    SET_LOW_WORD(s_h, 0);
    /* t_h=ax+bp[k] High */
    t_h = 0.0;
    SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
    t_l = ax - (t_h - bp[k]);
    s_l = v * ((u - s_h * t_h) - s_h * t_l);
    /* compute log(ax) */
    s2 = ss * ss;
    r = s2 * s2 *
        (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
    r += s_l * (s_h + ss);
    s2 = s_h * s_h;
    t_h = 3.0 + s2 + r;
    SET_LOW_WORD(t_h, 0);
    t_l = r - ((t_h - 3.0) - s2);
    /* u+v = ss*(1+...) */
    u = s_h * t_h;
    v = s_l * t_h + t_l * ss;
    /* 2/(3log2)*(ss+...) */
    p_h = u + v;
    SET_LOW_WORD(p_h, 0);
    p_l = v - (p_h - u);
    z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
    z_l = cp_l * p_h + p_l * cp + dp_l[k];
    /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
    t = (double)n;
    t1 = ((z_h + z_l) + dp_h[k]) + t;
    SET_LOW_WORD(t1, 0);
    t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
  }

  /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
  y1 = y;
  SET_LOW_WORD(y1, 0);
  p_l = (y - y1) * t1 + y * t2;
  p_h = y1 * t1;
  z = p_l + p_h;
  EXTRACT_WORDS(j, i, z);
  if (j >= 0x40900000) {                             /* z >= 1024 */
    if (((j - 0x40900000) | i) != 0)                 /* if z > 1024 */
      return s * huge * huge;                        /* overflow */
    if (p_l + ovt > z - p_h) return s * huge * huge; /* overflow */
  } else if ((j & 0x7fffffff) >= 0x4090cc00) {       /* z <= -1075 */
    if (((j - 0xc090cc00) | i) != 0)                 /* z < -1075 */
      return s * tiny * tiny;                        /* underflow */
    if (p_l <= z - p_h) return s * tiny * tiny;      /* underflow */
  }
  /*
   * compute 2**(p_h+p_l)
   */
  i = j & 0x7fffffff;
  k = (i >> 20) - 0x3ff;
  n = 0;
  if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
    n = j + (0x00100000 >> (k + 1));
    k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
    t = 0.0;
    SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
    n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
    if (j < 0) n = -n;
    p_h -= t;
  }
  t = p_l + p_h;
  SET_LOW_WORD(t, 0);
  u = t * lg2_h;
  v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
  z = u + v;
  w = v - (z - u);
  t = z * z;
  t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
  r = (z * t1) / (t1 - 2.0) - (w + z * w);
  z = 1.0 - (r - z);
  GET_HIGH_WORD(j, z);
  j += n << 20;
  if ((j >> 20) <= 0) /* subnormal output */
    z = scalbn(z, n);
  else
    SET_HIGH_WORD(z, j);
  return s * z;
}

double sqrt(double x) {
  double z;
  int32_t sign = (int)0x80000000;
  int32_t ix0, s0, q, m, t, i;
  uint32_t r, t1, s1, ix1, q1;

  EXTRACT_WORDS(ix0, ix1, x);

  /* take care of Inf and NaN */
  if ((ix0 & 0x7ff00000) == 0x7ff00000) {
    return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
  }
  /* take care of zero */
  if (ix0 <= 0) {
    if (((ix0 & ~sign) | ix1) == 0) return x; /* sqrt(+-0) = +-0 */
    if (ix0 < 0) return (x - x) / (x - x);    /* sqrt(-ve) = sNaN */
  }
  /* normalize x */
  m = ix0 >> 20;
  if (m == 0) { /* subnormal x */
    while (ix0 == 0) {
      m -= 21;
      ix0 |= (ix1 >> 11);
      ix1 <<= 21;
    }
    for (i = 0; (ix0 & 0x00100000) == 0; i++) ix0 <<= 1;
    m -= i - 1;
    ix0 |= ix1 >> (32 - i);
    ix1 <<= i;
  }
  m -= 1023; /* unbias exponent */
  ix0 = (ix0 & 0x000fffff) | 0x00100000;
  if (m & 1) { /* odd m, double x to make it even */
    ix0 += ix0 + ((ix1 & sign) >> 31);
    ix1 += ix1;
  }
  m >>= 1; /* m = [m/2] */

  /* generate sqrt(x) bit by bit */
  ix0 += ix0 + ((ix1 & sign) >> 31);
  ix1 += ix1;
  q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
  r = 0x00200000;       /* r = moving bit from right to left */

  while (r != 0) {
    t = s0 + r;
    if (t <= ix0) {
      s0 = t + r;
      ix0 -= t;
      q += r;
    }
    ix0 += ix0 + ((ix1 & sign) >> 31);
    ix1 += ix1;
    r >>= 1;
  }

  r = sign;
  while (r != 0) {
    t1 = s1 + r;
    t = s0;
    if (t < ix0 || (t == ix0 && t1 <= ix1)) {
      s1 = t1 + r;
      if ((t1 & sign) == sign && (s1 & sign) == 0) s0++;
      ix0 -= t;
      if (ix1 < t1) ix0--;
      ix1 -= t1;
      q1 += r;
    }
    ix0 += ix0 + ((ix1 & sign) >> 31);
    ix1 += ix1;
    r >>= 1;
  }

  /* use floating add to find out rounding direction */
  if ((ix0 | ix1) != 0) {
    z = 1.0 - tiny; /* raise inexact flag */
    if (z >= 1.0) {
      z = 1.0 + tiny;
      if (q1 == (uint32_t)0xffffffff) {
        q1 = 0;
        q++;
      } else if (z > 1.0) {
        if (q1 == (uint32_t)0xfffffffe) q++;
        q1 += 2;
      } else
        q1 += q1 & 1;
    }
  }
  ix0 = (q >> 1) + 0x3fe00000;
  ix1 = q1 >> 1;
  if (q & 1) ix1 |= sign;
  ix0 += m << 20;
  INSERT_WORDS(z, ix0, ix1);
  return z;
}

double fabs(double x) {
  union {
    double f;
    uint64_t i;
  } u = {x};
  u.i &= -1ULL / 2;
  return u.f;
}

double scalbn(double x, int n) {
  union {
    double f;
    uint64_t i;
  } u;
  double_t y = x;

  if (n > 1023) {
    y *= 0x1p1023;
    n -= 1023;
    if (n > 1023) {
      y *= 0x1p1023;
      n -= 1023;
      if (n > 1023) n = 1023;
    }
  } else if (n < -1022) {
    y *= 0x1p-1022;
    n += 1022;
    if (n < -1022) {
      y *= 0x1p-1022;
      n += 1022;
      if (n < -1022) n = -1022;
    }
  }
  u.i = (uint64_t)(0x3ff + n) << 52;
  x = y * u.f;
  return x;
}